My primary research interests are in dynamics modeling, control and estimation of mobile robots, spacecraft and unmanned vehicles modeled as rigid body and multi-body systems. The framework of this research is based on geometric mechanics and geometric control. These methods provide the substantial practical advantage of Lyapunov stability in the control and estimation schemes obtained. A secondary practical advantage is that such schemes lead to energy-efficient and robust control that is implementable with current technology. Geometric mechanics is the study of the mechanics of systems that evolve on state spaces that may not be vector spaces. The overall (translational and attitude) motion of aerospace vehicles cannot be described globally on a vector space, as their states evolve on a differentiable manifold that cannot be continuously deformed to a vector space. For spacecraft, maneuverable aerial vehicles and several robotic systems, the large ranges of rotational motion necessitate a global analysis of the state space to tackle dynamics, state estimation and control problems of interest. The vast majority of current schemes for control and state estimation of such systems are either applicable to local motion due to singularities, or they are unstable in the sense of Lyapunov, or they require discontinuous or hybrid control schemes that cannot be implemented by attitude actuators that can only provide continuous inputs. Technical challenges that can be overcome with the nonlinear estimation and control techniques that I have developed include robustness to uncertainties in the dynamics; coupled control, power and communication constraints; actuator constraints; and control and estimation of system states and uncertain inputs over large ranges of possible motions.